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Fractional Hilbert transform extensions and associated analytic signal construction
Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India .ORCID iD: 0000-0003-1285-8947
Indian Institute of Science Bangalore. (Department of Electrical Engineering)
2014 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 94, 359-372 p.Article in journal (Refereed) Published
Abstract [en]

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations.

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 94, 359-372 p.
Keyword [en]
Hilbert transform, Fractional Hilbert transform, Analytic signal, Single-sideband modulation, Generalized-phase Hilbert transform, Generalized-phase analytic signal
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-131269DOI: 10.1016/j.sigpro.2013.05.009ISI: 000327363300039Scopus ID: 2-s2.0-84880902327OAI: oai:DiVA.org:kth-131269DiVA: diva2:655191
Note

QC 20140203

Available from: 2013-10-10 Created: 2013-10-10 Last updated: 2017-12-06Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf